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calculate the values of 2. f * x ^ 2 + y ^ 2 = 5/8 * and * 4/3 * xy = 1/4 (a) (x + y) (b) (x-y) (c) (x^2-y^2)​

Calculate The Values Of 2 F X 2 Y 2 58 And 43 Xy 14 A X Y B Xy C X2y2 class=

Sagot :

rvkacademic

Answer:

(a) 1

(b) 1/2

(c) 1/2

Step-by-step explanation:

[tex]x^2 + y^2 = 5/8 (1)\\\frac{4}{3}xy = \frac{1}{4} (2)\\\\\textrm {From (2) by multiplying both sides by 3/4 we get}\\\\xy = \frac{3}{16} (3)\\\textrm{We know that } (x + y)^2 = x^2 + 2xy + y^2 \\\textrm{Adding 2xy to the LHS and RHS of equation 1 gisues us }\\x^2 + y^2 + 2xy = \frac{5}{8} + 2 * \frac{3}{16} = \frac{5}{8} + \frac{3}{8} = \frac{8}{8} = 1[/tex]

[tex](x + y)^2 = 1 == > x+y = \sqrt{1} = 1\\\\(x - y)^2 = x^2 -2xy + y^2\\\\\textrm{Subtracting 2xy from both sides of Equation 1}\\x^2 + y^2 - 2xy = \frac{5}{8} - 2*\frac{3}{16} = \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} \\x-y = \sqrt{\frac{1}{4}} = \frac{1}{2}\\\\x^2 - y^2 = (x+y)(x-y) = 1 . \frac{1}{2} = \frac{1}{2}[/tex]

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